What are the small flying bugs near lamps in my home?

My first guess on the bugs in your home are typical flies. Generally they are merely attracted to the heat and if you turn off the lights inside they go away. On the other side, they may be gnats or moths. They could also be mosquitos which, either way, they can be very annoying.

They could be gnats, but if you keep fruit in your kitchen then the bugs are probably the common fruit fly. They like bananas, vinegar, and anything that might be fermenting that they can get to. They like to rest on lampshades and are drawn to light. Discard old fruit, and check your garbage can and disposal for flying insects.

If you have small bugs flying near your lamps, they are probably moths. Moths live by the lunar cycle, and so will try to get close to any kind of globular light source at night time-it's instinctive. Try keeping your lamps turned off for a while, and keep your outside doors shut to get rid of them.